document.write( "Question 1142077: Find the coordinate of the vertices and foci and
\n" ); document.write( "the equation of the asymptotes for the hyperbola
\n" ); document.write( "with the equation (y^2/16)-(x^2/25)=1
\n" ); document.write( "

Algebra.Com's Answer #762751 by ikleyn(52778)\"\" \"About 
You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            I will show you how to find the equations for the hyperbola's asymptotes.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "The hyperbola is given by equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"y%5E2%2F16\" - \"x%5E2%2F25\" = 1.     (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The equation for the asymptotes is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"y%5E2%2F16\" - \"x%5E2%2F25\" = 0.      (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is obtained from the standard equation of the hyperbola (1) replacing \"1\" in the right side of the hyperbola' standard equation by \"0\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The equation (2) deploys in two equations (3) and (4) below for the two straight asymptotes in this way\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"%28y%2F4+%2B+x%2F5%29%2A%28y%2F4+-+x%2F5%29\" = 0  =================>\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"y%2F4+%2B+x%2F5\" = 0    (3),   and\r\n" );
document.write( "\r\n" );
document.write( "    \"y%2F4+-+x%2F5\" = 0.   (4)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You can further transform these equations for asymptotes (3), (4) to any other appropriate equivalent form.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For similar problem, see my post at the link\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "    https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1142075.html\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "in the archive of this forum.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );